GCF of 221/34, 424/420
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 221/34, 424/420 i.e 1/7140 easily. The following is the detailed procedure to determine the greatest common factor of fractions 221/34, 424/420.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 221/34,424/420?
Given fractions are 221/34,424/420
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 221/34,424/420, numerators are 221,424
Denominators are 34,420
The GCF of 221,424 is 1 .
LCM of 34,420 is 7140.
The greatest common factor of 221/34,424/420 = [GCF of 221,424]/[LCM of 34,420]= 1/7140
Therefore, the GCF of 221/34,424/420 is 1/7140.
To find the highest common factor of 221,424, we have to find the factors of both numbers and list the highest common factor.
The factors of 221 are 1, 13, 17, 221
The factors of 424 are 1, 2, 4, 8, 53, 106, 212, 424
The HCF of 221,424 is 1.
Lets's calculate GCF of 221,424
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 221,424 By Matching Biggest Common Factor Method
Now, list down the factors of 221
:1,13,17,221
Now, list down the factors of 424
:1,2,4,8,53,106,212,424
Greatest Common Factor
We found the factors 221,424 . The biggest common factor number is the GCF number.
So the greatest common factor 221,424 is 1.
Lets's calculate LCM of 34,420
| 2 | 34, 420 |
| 17, 210 |
∴ So the LCM of the given numbers is 2 x 17 x 210 = 7140
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/7140
Therefore, the GCF of Fractions 221/34,424/420 is 1/7140
Least Common Multiple of 34,420 with GCF Formula
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 34,420 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(34,420) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(34,420) x common factors =2 x 1 = 2
LCM(34,420) = ( 34 × 420 ) / 2
LCM(34,420) = 14280 / 2
LCM(34,420) = 7140
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FAQs on GCF of Fractions of 221/34, 424/420
1. What is the HCF of 221,424?
The HCF of 221,424 is 1
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
4. What is the GCF of Fractions for 221/34, 424/420?
Answer: GCF of Numerators as per given numbers 221/34, 424/420 is
GCF of Numerators i.e. for 221,424 is 1
LCM of denominators i.e. for 34,420 is 7140.
Thus, GCF of Fractions is 1/7140.Finally, GCF of Fractions for 221/34, 424/420 is 1/7140.